Tritium is an important nuclear fuel in fusion reactors and one of the dominant nuclides in the primary coolant in fission reactors. The storage, feeding, control, monitoring, and transport of tritium are important for practical engineering applications. Because of the high mobility of tritium in both fission and fusion nuclear systems and its effect on human body, tritium has received great attention worldwide. The retention and prevention of tritium permeation from primary loop to secondary loop is a common research interest in various reactors. Previous studies indicated that a surface oxide layer is an efficient method to reduce tritium permeation. In this paper, we summarize the effects of various oxide layers on the permeation of hydrogen isotopes in nuclear reactors. The permeation reduction factor for materials used in fusion reactors ranges from 1000 to 100000. The diffusion behavior of tritium in several materials with and without oxide layer is discussed in detail. The oxide layer is more important than intrinsic permeability to prevent tritium permeation. As tritium is the only radioactive source term in the secondary loop of high temperature gas-cooled reactors, we also reviewed the permeation of hydrogen isotopes in the heat exchanger, which is an important issue in nuclear hydrogen production. The present study provides a comprehensive overview of tritium permeation behavior and is expected to promote the development and design of tritium-permeation-proof materials in the future.